Estadistica y Probabilidad

Discretas

Generacion de Binomial

p = 0.30

N = 100

n1 <- 100
k <- 25
p <- 0.3

mibinomial_p3_100 <- rbinom(n1,k,p)

plot(mibinomial_p3_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p3_100, main="Histograma 100 VA Binom(k,p))",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 500

n2 <- 500
k <- 25
p <- 0.3

mibinomial_p3_500 <- rbinom(n2,k,p)

plot(mibinomial_p3_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p3_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 1000

n3 <- 1000
k <- 25
p <- 0.3

mibinomial_p3_1000 <- rbinom(n3,k,p)

plot(mibinomial_p3_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p3_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 5000

n4 <- 5000
k <- 25
p <- 0.3

mibinomial_p3_5000 <- rbinom(n4,k,p)

plot(mibinomial_p3_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p3_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 10000

n5 <- 10000
k <- 25
p <- 0.3

mibinomial_p3_10000 <- rbinom(n5,k,p)

plot(mibinomial_p3_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p3_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

p = 0.45

N = 100

n1 <- 100
k <- 25
p <- 0.45

mibinomial_p45_100 <- rbinom(n1,k,p)

plot(mibinomial_p45_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p45_100, main="Histograma 100 VA Binom(k,p))",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 500

n2 <- 500
k <- 25
p <- 0.45

mibinomial_p45_500 <- rbinom(n2,k,p)

plot(mibinomial_p45_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p45_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 1000

n3 <- 1000
k <- 25
p <- 0.45

mibinomial_p45_1000 <- rbinom(n3,k,p)

plot(mibinomial_p45_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p45_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 5000

n4 <- 5000
k <- 25
p <- 0.45

mibinomial_p45_5000 <- rbinom(n4,k,p)

plot(mibinomial_p45_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p45_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 10000

n5 <- 10000
k <- 25
p <- 0.45

mibinomial_p45_10000 <- rbinom(n5,k,p)

plot(mibinomial_p45_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p45_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

p = 0.8

N = 100

n1 <- 100
k <- 25
p <- 0.8

mibinomial_p8_100 <- rbinom(n1,k,p)

plot(mibinomial_p8_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p8_100, main="Histograma 100 VA Binom(k,p))",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 500

n2 <- 500
k <- 25
p <- 0.8

mibinomial_p8_500 <- rbinom(n2,k,p)

plot(mibinomial_p8_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p8_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 1000

n3 <- 1000
k <- 25
p <- 0.8

mibinomial_p8_1000 <- rbinom(n3,k,p)

plot(mibinomial_p8_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p8_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 5000

n4 <- 5000
k <- 25
p <- 0.8

mibinomial_p8_5000 <- rbinom(n4,k,p)

plot(mibinomial_p8_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p8_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 10000

n5 <- 10000
k <- 25
p <- 0.8

mibinomial_p8_10000 <- rbinom(n5,k,p)

plot(mibinomial_p8_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p8_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

p = 0.96

N = 100

n1 <- 100
k <- 25
p <- 0.96

mibinomial_p96_100 <- rbinom(n1,k,p)

plot(mibinomial_p96_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p96_100, main="Histograma 100 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 500

n2 <- 500
k <- 25
p <- 0.96

mibinomial_p96_500 <- rbinom(n2,k,p)

plot(mibinomial_p96_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p96_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 1000

n3 <- 1000
k <- 25
p <- 0.96

mibinomial_p96_1000 <- rbinom(n3,k,p)

plot(mibinomial_p96_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p96_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 5000

n4 <- 5000
k <- 25
p <- 0.96

mibinomial_p96_5000 <- rbinom(n4,k,p)

plot(mibinomial_p96_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p96_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

N = 10000

n5 <- 10000
k <- 25
p <- 0.96

mibinomial_p96_10000 <- rbinom(n5,k,p)

plot(mibinomial_p96_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,p)")

hist(mibinomial_p96_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,p)")

Comparacion de graficos Plot

Comparando plot de N = 100

par(mfrow = c(2,2))
plot(mibinomial_p3_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
plot(mibinomial_p45_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
plot(mibinomial_p8_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
plot(mibinomial_p96_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando plot de N = 500

par(mfrow = c(2,2))
plot(mibinomial_p3_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
plot(mibinomial_p45_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
plot(mibinomial_p8_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
plot(mibinomial_p96_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando plot de N = 1000

par(mfrow = c(2,2))
plot(mibinomial_p3_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
plot(mibinomial_p45_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
plot(mibinomial_p8_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
plot(mibinomial_p96_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando plot de N = 5000

par(mfrow = c(2,2))
plot(mibinomial_p3_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
plot(mibinomial_p45_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
plot(mibinomial_p8_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
plot(mibinomial_p96_5000,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando plot de N = 10000

par(mfrow = c(2,2))
plot(mibinomial_p3_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
plot(mibinomial_p45_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
plot(mibinomial_p8_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
plot(mibinomial_p96_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparacion de graficos Hist

Comparando hist de N = 100

par(mfrow = c(2,2))
hist(mibinomial_p3_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
hist(mibinomial_p45_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
hist(mibinomial_p8_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
hist(mibinomial_p96_100,col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando hist de N = 500

par(mfrow = c(2,2))
hist(mibinomial_p3_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
hist(mibinomial_p45_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
hist(mibinomial_p8_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
hist(mibinomial_p96_500,col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando hist de N = 1000

par(mfrow = c(2,2))
hist(mibinomial_p3_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
hist(mibinomial_p45_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
hist(mibinomial_p8_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
hist(mibinomial_p96_1000,col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando hist de N = 5000

par(mfrow = c(2,2))
hist(mibinomial_p3_500,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
hist(mibinomial_p45_500,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
hist(mibinomial_p8_500,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
hist(mibinomial_p96_500,col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

Comparando hist de N = 10000

par(mfrow = c(2,2))
hist(mibinomial_p3_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.30)")
hist(mibinomial_p45_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.45)")
hist(mibinomial_p8_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.80)")
hist(mibinomial_p96_10000,col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.96)")

k = 10

N = 100

n1 <- 100
k <- 10
p <- 0.5

mibinomial_k10_100 <- rbinom(n1, k, p)

plot(mibinomial_k10_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")

hist(mibinomial_k10_100, main="Histograma 100 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(10,0.5)")

N = 500

n2 <- 500
k <- 10
p <- 0.5

mibinomial_k10_500 <- rbinom(n2, k, p)

plot(mibinomial_k10_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")

hist(mibinomial_k10_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(10,0.5)")

N = 1000

n3 <- 1000
k <- 10
p <- 0.5

mibinomial_k10_1000 <- rbinom(n3, k, p)

plot(mibinomial_k10_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")

hist(mibinomial_k10_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(10,0.5)")

N = 5000

n4 <- 5000
k <- 10
p <- 0.5

mibinomial_k10_5000 <- rbinom(n4, k, p)

plot(mibinomial_k10_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")

hist(mibinomial_k10_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(10,0.5)")

N = 10000

n5 <- 10000
k <- 10
p <- 0.5

mibinomial_k10_10000 <- rbinom(n5, k, p)

plot(mibinomial_k10_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")

hist(mibinomial_k10_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(10,0.5)")

k = 25

N = 100

n1 <- 100
k <- 25
p <- 0.5

mibinomial_k25_100 <- rbinom(n1, k, p)

plot(mibinomial_k25_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")

hist(mibinomial_k25_100, main="Histograma 100 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,0.5)")

N = 500

n2 <- 500
k <- 25
p <- 0.5

mibinomial_k25_500 <- rbinom(n2, k, p)

plot(mibinomial_k25_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")

hist(mibinomial_k25_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,0.5)")

N = 1000

n3 <- 1000
k <- 25
p <- 0.5

mibinomial_k25_1000 <- rbinom(n3, k, p)

plot(mibinomial_k25_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")

hist(mibinomial_k25_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,0.5)")

N = 5000

n4 <- 5000
k <- 25
p <- 0.5

mibinomial_k25_5000 <- rbinom(n4, k, p)

plot(mibinomial_k25_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")

hist(mibinomial_k25_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,0.5)")

N = 10000

n5 <- 10000
k <- 25
p <- 0.5

mibinomial_k25_10000 <- rbinom(n5, k, p)

plot(mibinomial_k25_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")

hist(mibinomial_k25_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(25,0.5)")

k = 50

N = 100

n1 <- 100
k <- 50
p <- 0.5

mibinomial_k50_100 <- rbinom(n1, k, p)

plot(mibinomial_k50_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")

hist(mibinomial_k50_100, main="Histograma 100 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(50,0.5)")

N = 500

n2 <- 500
k <- 50
p <- 0.5

mibinomial_k50_500 <- rbinom(n2, k, p)

plot(mibinomial_k50_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")

hist(mibinomial_k50_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(50,0.5)")

N = 1000

n3 <- 1000
k <- 50
p <- 0.5

mibinomial_k50_1000 <- rbinom(n3, k, p)

plot(mibinomial_k50_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")

hist(mibinomial_k50_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(50,0.5)")

N = 5000

n4 <- 5000
k <- 50
p <- 0.5

mibinomial_k50_5000 <- rbinom(n4, k, p)

plot(mibinomial_k50_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")

hist(mibinomial_k50_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(50,0.5)")

N = 10000

n5 <- 10000
k <- 50
p <- 0.5

mibinomial_k50_10000 <- rbinom(n5, k, p)

plot(mibinomial_k50_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")

hist(mibinomial_k50_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(50,0.5)")

k = 100

N = 100

n1 <- 100
k <- 100
p <- 0.5

mibinomial_k100_100 <- rbinom(n1, k, p)

plot(mibinomial_k100_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

hist(mibinomial_k100_100, main="Histograma 100 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(100,0.5)")

N = 500

n2 <- 500
k <- 100
p <- 0.5

mibinomial_k100_500 <- rbinom(n2, k, p)

plot(mibinomial_k100_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

hist(mibinomial_k100_500, main="Histograma 500 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(100,0.5)")

N = 1000

n3 <- 1000
k <- 100
p <- 0.5

mibinomial_k100_1000 <- rbinom(n3, k, p)

plot(mibinomial_k100_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

hist(mibinomial_k100_1000, main="Histograma 1000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(100,0.5)")

N = 5000

n4 <- 5000
k <- 100
p <- 0.5

mibinomial_k100_5000 <- rbinom(n4, k, p)

plot(mibinomial_k100_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

hist(mibinomial_k100_5000, main="Histograma 5000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(100,0.5)")

N = 10000

n5 <- 10000
k <- 100
p <- 0.5

mibinomial_k100_10000 <- rbinom(n5, k, p)

plot(mibinomial_k100_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

hist(mibinomial_k100_10000, main="Histograma 10000 VA Binom(k,p)",
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = "Binom(100,0.5)")

Comparacion de gráficos Plot

Comparando plot de N = 100

par(mfrow = c(2,2))
plot(mibinomial_k10_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
plot(mibinomial_k25_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
plot(mibinomial_k50_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
plot(mibinomial_k100_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando plot de N = 500

par(mfrow = c(2,2))
plot(mibinomial_k10_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
plot(mibinomial_k25_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
plot(mibinomial_k50_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
plot(mibinomial_k100_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando plot de N = 1000

par(mfrow = c(2,2))
plot(mibinomial_k10_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
plot(mibinomial_k25_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
plot(mibinomial_k50_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
plot(mibinomial_k100_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando plot de N = 5000

par(mfrow = c(2,2))
plot(mibinomial_k10_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
plot(mibinomial_k25_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
plot(mibinomial_k50_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
plot(mibinomial_k100_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando plot de N = 10000

par(mfrow = c(2,2))
plot(mibinomial_k10_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
plot(mibinomial_k25_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
plot(mibinomial_k50_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
plot(mibinomial_k100_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparacion de gráficos Hist

Comparando hist de N = 100

par(mfrow = c(2,2))
hist(mibinomial_k10_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
hist(mibinomial_k25_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
hist(mibinomial_k50_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
hist(mibinomial_k100_100, col="blue",
     main = "100 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando hist de N = 500

par(mfrow = c(2,2))
hist(mibinomial_k10_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
hist(mibinomial_k25_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
hist(mibinomial_k50_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
hist(mibinomial_k100_500, col="blue",
     main = "500 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando hist de N = 1000

par(mfrow = c(2,2))
hist(mibinomial_k10_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
hist(mibinomial_k25_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
hist(mibinomial_k50_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
hist(mibinomial_k100_1000, col="blue",
     main = "1000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando hist de N = 5000

par(mfrow = c(2,2))
hist(mibinomial_k10_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
hist(mibinomial_k25_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
hist(mibinomial_k50_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
hist(mibinomial_k100_5000, col="blue",
     main = "5000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

Comparando hist de N = 10000

par(mfrow = c(2,2))
hist(mibinomial_k10_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(10,0.5)")
hist(mibinomial_k25_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(25,0.5)")
hist(mibinomial_k50_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(50,0.5)")
hist(mibinomial_k100_10000, col="blue",
     main = "10000 VA Binom(k,p)",
     xlab="Num de VA",
     ylab = "Binom(100,0.5)")

En conclusión Binomial

• m : Representa el número total de experimentos completos que realizamos. Es decir, cuántas veces llevamos a cabo el conjunto de ensayos.

• k: Indica cuántas veces ocurre el evento de interés (los llamados “éxitos”) dentro de esos experimentos. Se utiliza para calcular la probabilidad de observar exactamente ese número de ocurrencias.

• p: Es la probabilidad de que ocurra el evento en un solo ensayo individual. Esta probabilidad se mantiene constante en cada repetición, lo que garantiza que la distribución binomial pueda aplicarse correctamente.

Generación de Poisson

λ = 0.15

N = 100

n1 <- 100
milambda <- 0.15

mipoisson_l015_100 <- rpois(n1, milambda)

etiqueta_Y <- paste0("Poisson(", n1, ",", milambda, ")")
mititulo <- paste0(n1, " VA Pois(", milambda, ")")
plot(mipoisson_l015_100, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n1, " VA Pois(", milambda, ")")
hist(mipoisson_l015_100, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 500

n2 <- 500
milambda <- 0.15

mipoisson_l015_500 <- rpois(n2, milambda)

etiqueta_Y <- paste0("Poisson(", n2, ",", milambda, ")")
mititulo <- paste0(n2, " VA Pois(", milambda, ")")
plot(mipoisson_l015_500, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n2, " VA Pois(", milambda, ")")
hist(mipoisson_l015_500, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 1000

n3 <- 1000
milambda <- 0.15

mipoisson_l015_1000 <- rpois(n3, milambda)

etiqueta_Y <- paste0("Poisson(", n3, ",", milambda, ")")
mititulo <- paste0(n3, " VA Pois(", milambda, ")")
plot(mipoisson_l015_1000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n3, " VA Pois(", milambda, ")")
hist(mipoisson_l015_1000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 5000

n4 <- 5000
milambda <- 0.15

mipoisson_l015_5000 <- rpois(n4, milambda)

etiqueta_Y <- paste0("Poisson(", n4, ",", milambda, ")")
mititulo <- paste0(n4, " VA Pois(", milambda, ")")
plot(mipoisson_l015_5000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n4, " VA Pois(", milambda, ")")
hist(mipoisson_l015_5000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 10000

n5 <- 10000
milambda <- 0.15

mipoisson_l015_10000 <- rpois(n5, milambda)

etiqueta_Y <- paste0("Poisson(", n5, ",", milambda, ")")
mititulo <- paste0(n5, " VA Pois(", milambda, ")")
plot(mipoisson_l015_10000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n5, " VA Pois(", milambda, ")")
hist(mipoisson_l015_10000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 15000

n6 <- 15000
milambda <- 0.15

mipoisson_l015_15000 <- rpois(n6, milambda)

etiqueta_Y <- paste0("Poisson(", n6, ",", milambda, ")")
mititulo <- paste0(n6, " VA Pois(", milambda, ")")
plot(mipoisson_l015_15000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n6, " VA Pois(", milambda, ")")
hist(mipoisson_l015_15000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

λ = 0.30

N = 100

n1 <- 100
milambda <- 0.30

mipoisson_l030_100 <- rpois(n1, milambda)

etiqueta_Y <- paste0("Poisson(", n1, ",", milambda, ")")
mititulo <- paste0(n1, " VA Pois(", milambda, ")")
plot(mipoisson_l030_100, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n1, " VA Pois(", milambda, ")")
hist(mipoisson_l030_100, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 500

n2 <- 500
milambda <- 0.30

mipoisson_l030_500 <- rpois(n2, milambda)

etiqueta_Y <- paste0("Poisson(", n2, ",", milambda, ")")
mititulo <- paste0(n2, " VA Pois(", milambda, ")")
plot(mipoisson_l030_500, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n2, " VA Pois(", milambda, ")")
hist(mipoisson_l030_500, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 1000

n3 <- 1000
milambda <- 0.30

mipoisson_l030_1000 <- rpois(n3, milambda)

etiqueta_Y <- paste0("Poisson(", n3, ",", milambda, ")")
mititulo <- paste0(n3, " VA Pois(", milambda, ")")
plot(mipoisson_l030_1000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n3, " VA Pois(", milambda, ")")
hist(mipoisson_l030_1000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 5000

n4 <- 5000
milambda <- 0.30

mipoisson_l030_5000 <- rpois(n4, milambda)

etiqueta_Y <- paste0("Poisson(", n4, ",", milambda, ")")
mititulo <- paste0(n4, " VA Pois(", milambda, ")")
plot(mipoisson_l030_5000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n4, " VA Pois(", milambda, ")")
hist(mipoisson_l030_5000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 10000

n5 <- 10000
milambda <- 0.30

mipoisson_l030_10000 <- rpois(n5, milambda)

etiqueta_Y <- paste0("Poisson(", n5, ",", milambda, ")")
mititulo <- paste0(n5, " VA Pois(", milambda, ")")
plot(mipoisson_l030_10000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n5, " VA Pois(", milambda, ")")
hist(mipoisson_l030_10000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 15000

n6 <- 15000
milambda <- 0.30

mipoisson_l030_15000 <- rpois(n6, milambda)

etiqueta_Y <- paste0("Poisson(", n6, ",", milambda, ")")
mititulo <- paste0(n6, " VA Pois(", milambda, ")")
plot(mipoisson_l030_15000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n6, " VA Pois(", milambda, ")")
hist(mipoisson_l030_15000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

λ = 0.5

N = 100

n1 <- 100
milambda <- 0.5

mipoisson_l05_100 <- rpois(n1, milambda)

etiqueta_Y <- paste0("Poisson(", n1, ",", milambda, ")")
mititulo <- paste0(n1, " VA Pois(", milambda, ")")
plot(mipoisson_l05_100, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n1, " VA Pois(", milambda, ")")
hist(mipoisson_l05_100, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 500

n2 <- 500
milambda <- 0.5

mipoisson_l05_500 <- rpois(n2, milambda)

etiqueta_Y <- paste0("Poisson(", n2, ",", milambda, ")")
mititulo <- paste0(n2, " VA Pois(", milambda, ")")
plot(mipoisson_l05_500, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n2, " VA Pois(", milambda, ")")
hist(mipoisson_l05_500, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 1000

n3 <- 1000
milambda <- 0.5

mipoisson_l05_1000 <- rpois(n3, milambda)

etiqueta_Y <- paste0("Poisson(", n3, ",", milambda, ")")
mititulo <- paste0(n3, " VA Pois(", milambda, ")")
plot(mipoisson_l05_1000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n3, " VA Pois(", milambda, ")")
hist(mipoisson_l05_1000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 5000

n4 <- 5000
milambda <- 0.5

mipoisson_l05_5000 <- rpois(n4, milambda)

etiqueta_Y <- paste0("Poisson(", n4, ",", milambda, ")")
mititulo <- paste0(n4, " VA Pois(", milambda, ")")
plot(mipoisson_l05_5000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n4, " VA Pois(", milambda, ")")
hist(mipoisson_l05_5000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 10000

n5 <- 10000
milambda <- 0.5

mipoisson_l05_10000 <- rpois(n5, milambda)

etiqueta_Y <- paste0("Poisson(", n5, ",", milambda, ")")
mititulo <- paste0(n5, " VA Pois(", milambda, ")")
plot(mipoisson_l05_10000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n5, " VA Pois(", milambda, ")")
hist(mipoisson_l05_10000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 15000

n6 <- 15000
milambda <- 0.5

mipoisson_l05_15000 <- rpois(n6, milambda)

etiqueta_Y <- paste0("Poisson(", n6, ",", milambda, ")")
mititulo <- paste0(n6, " VA Pois(", milambda, ")")
plot(mipoisson_l05_15000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n6, " VA Pois(", milambda, ")")
hist(mipoisson_l05_15000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

λ = 0.70

N = 100

n1 <- 100
milambda <- 0.70

mipoisson_l070_100 <- rpois(n1, milambda)

etiqueta_Y <- paste0("Poisson(", n1, ",", milambda, ")")
mititulo <- paste0(n1, " VA Pois(", milambda, ")")
plot(mipoisson_l070_100, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n1, " VA Pois(", milambda, ")")
hist(mipoisson_l070_100, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 500

n2 <- 500
milambda <- 0.70

mipoisson_l070_500 <- rpois(n2, milambda)

etiqueta_Y <- paste0("Poisson(", n2, ",", milambda, ")")
mititulo <- paste0(n2, " VA Pois(", milambda, ")")
plot(mipoisson_l070_500, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n2, " VA Pois(", milambda, ")")
hist(mipoisson_l070_500, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 1000

n3 <- 1000
milambda <- 0.70

mipoisson_l070_1000 <- rpois(n3, milambda)

etiqueta_Y <- paste0("Poisson(", n3, ",", milambda, ")")
mititulo <- paste0(n3, " VA Pois(", milambda, ")")
plot(mipoisson_l070_1000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n3, " VA Pois(", milambda, ")")
hist(mipoisson_l070_1000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 5000

n4 <- 5000
milambda <- 0.70

mipoisson_l070_5000 <- rpois(n4, milambda)

etiqueta_Y <- paste0("Poisson(", n4, ",", milambda, ")")
mititulo <- paste0(n4, " VA Pois(", milambda, ")")
plot(mipoisson_l070_5000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n4, " VA Pois(", milambda, ")")
hist(mipoisson_l070_5000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 10000

n5 <- 10000
milambda <- 0.70

mipoisson_l070_10000 <- rpois(n5, milambda)

etiqueta_Y <- paste0("Poisson(", n5, ",", milambda, ")")
mititulo <- paste0(n5, " VA Pois(", milambda, ")")
plot(mipoisson_l070_10000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n5, " VA Pois(", milambda, ")")
hist(mipoisson_l070_10000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 15000

n6 <- 15000
milambda <- 0.70

mipoisson_l070_15000 <- rpois(n6, milambda)

etiqueta_Y <- paste0("Poisson(", n6, ",", milambda, ")")
mititulo <- paste0(n6, " VA Pois(", milambda, ")")
plot(mipoisson_l070_15000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n6, " VA Pois(", milambda, ")")
hist(mipoisson_l070_15000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

λ = 0.85

N = 100

n1 <- 100
milambda <- 0.85

mipoisson_l085_100 <- rpois(n1, milambda)

etiqueta_Y <- paste0("Poisson(", n1, ",", milambda, ")")
mititulo <- paste0(n1, " VA Pois(", milambda, ")")
plot(mipoisson_l085_100, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n1, " VA Pois(", milambda, ")")
hist(mipoisson_l085_100, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 500

n2 <- 500
milambda <- 0.85

mipoisson_l085_500 <- rpois(n2, milambda)

etiqueta_Y <- paste0("Poisson(", n2, ",", milambda, ")")
mititulo <- paste0(n2, " VA Pois(", milambda, ")")
plot(mipoisson_l085_500, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n2, " VA Pois(", milambda, ")")
hist(mipoisson_l085_500, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 1000

n3 <- 1000
milambda <- 0.85

mipoisson_l085_1000 <- rpois(n3, milambda)

etiqueta_Y <- paste0("Poisson(", n3, ",", milambda, ")")
mititulo <- paste0(n3, " VA Pois(", milambda, ")")
plot(mipoisson_l085_1000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n3, " VA Pois(", milambda, ")")
hist(mipoisson_l085_1000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 5000

n4 <- 5000
milambda <- 0.85

mipoisson_l085_5000 <- rpois(n4, milambda)

etiqueta_Y <- paste0("Poisson(", n4, ",", milambda, ")")
mititulo <- paste0(n4, " VA Pois(", milambda, ")")
plot(mipoisson_l085_5000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n4, " VA Pois(", milambda, ")")
hist(mipoisson_l085_5000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 10000

n5 <- 10000
milambda <- 0.85

mipoisson_l085_10000 <- rpois(n5, milambda)

etiqueta_Y <- paste0("Poisson(", n5, ",", milambda, ")")
mititulo <- paste0(n5, " VA Pois(", milambda, ")")
plot(mipoisson_l085_10000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n5, " VA Pois(", milambda, ")")
hist(mipoisson_l085_10000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

N = 15000

n6 <- 15000
milambda <- 0.85

mipoisson_l085_15000 <- rpois(n6, milambda)

etiqueta_Y <- paste0("Poisson(", n6, ",", milambda, ")")
mititulo <- paste0(n6, " VA Pois(", milambda, ")")
plot(mipoisson_l085_15000, col="blue",
     main = mititulo,
     xlab = "Num de VA",
     ylab = etiqueta_Y)

mititulo <- paste0("Histograma ", n6, " VA Pois(", milambda, ")")
hist(mipoisson_l085_15000, main = mititulo,
     col = "lightgreen",
     xlab = "VA generadas",
     ylab = etiqueta_Y)

Comparación de gráficos Plot

Comparando plot de N = 100

par(mfrow = c(3,2))
plot(mipoisson_l015_100, col="blue", main = "100 VA Pois(0.15)", xlab="Num de VA", ylab = "Poisson(100,0.15)")
plot(mipoisson_l030_100, col="blue", main = "100 VA Pois(0.30)", xlab="Num de VA", ylab = "Poisson(100,0.30)")
plot(mipoisson_l05_100, col="blue", main = "100 VA Pois(0.5)", xlab="Num de VA", ylab = "Poisson(100,0.5)")
plot(mipoisson_l070_100, col="blue", main = "100 VA Pois(0.70)", xlab="Num de VA", ylab = "Poisson(100,0.70)")
plot(mipoisson_l085_100, col="blue", main = "100 VA Pois(0.85)", xlab="Num de VA", ylab = "Poisson(100,0.85)")

Comparando plot de N = 500

par(mfrow = c(3,2))
plot(mipoisson_l015_500, col="blue", main = "500 VA Pois(0.15)", xlab="Num de VA", ylab = "Poisson(500,0.15)")
plot(mipoisson_l030_500, col="blue", main = "500 VA Pois(0.30)", xlab="Num de VA", ylab = "Poisson(500,0.30)")
plot(mipoisson_l05_500, col="blue", main = "500 VA Pois(0.5)", xlab="Num de VA", ylab = "Poisson(500,0.5)")
plot(mipoisson_l070_500, col="blue", main = "500 VA Pois(0.70)", xlab="Num de VA", ylab = "Poisson(500,0.70)")
plot(mipoisson_l085_500, col="blue", main = "500 VA Pois(0.85)", xlab="Num de VA", ylab = "Poisson(500,0.85)")

Comparando plot de N = 1000

par(mfrow = c(3,2))
plot(mipoisson_l015_1000, col="blue", main = "1000 VA Pois(0.15)", xlab="Num de VA", ylab = "Poisson(1000,0.15)")
plot(mipoisson_l030_1000, col="blue", main = "1000 VA Pois(0.30)", xlab="Num de VA", ylab = "Poisson(1000,0.30)")
plot(mipoisson_l05_1000, col="blue", main = "1000 VA Pois(0.5)", xlab="Num de VA", ylab = "Poisson(1000,0.5)")
plot(mipoisson_l070_1000, col="blue", main = "1000 VA Pois(0.70)", xlab="Num de VA", ylab = "Poisson(1000,0.70)")
plot(mipoisson_l085_1000, col="blue", main = "1000 VA Pois(0.85)", xlab="Num de VA", ylab = "Poisson(1000,0.85)")

Comparando plot de N = 5000

par(mfrow = c(3,2))
plot(mipoisson_l015_5000, col="blue", main = "5000 VA Pois(0.15)", xlab="Num de VA", ylab = "Poisson(5000,0.15)")
plot(mipoisson_l030_5000, col="blue", main = "5000 VA Pois(0.30)", xlab="Num de VA", ylab = "Poisson(5000,0.30)")
plot(mipoisson_l05_5000, col="blue", main = "5000 VA Pois(0.5)", xlab="Num de VA", ylab = "Poisson(5000,0.5)")
plot(mipoisson_l070_5000, col="blue", main = "5000 VA Pois(0.70)", xlab="Num de VA", ylab = "Poisson(5000,0.70)")
plot(mipoisson_l085_5000, col="blue", main = "5000 VA Pois(0.85)", xlab="Num de VA", ylab = "Poisson(5000,0.85)")

Comparando plot de N = 10000

par(mfrow = c(3,2))
plot(mipoisson_l015_10000, col="blue", main = "10000 VA Pois(0.15)", xlab="Num de VA", ylab = "Poisson(10000,0.15)")
plot(mipoisson_l030_10000, col="blue", main = "10000 VA Pois(0.30)", xlab="Num de VA", ylab = "Poisson(10000,0.30)")
plot(mipoisson_l05_10000, col="blue", main = "10000 VA Pois(0.5)", xlab="Num de VA", ylab = "Poisson(10000,0.5)")
plot(mipoisson_l070_10000, col="blue", main = "10000 VA Pois(0.70)", xlab="Num de VA", ylab = "Poisson(10000,0.70)")
plot(mipoisson_l085_10000, col="blue", main = "10000 VA Pois(0.85)", xlab="Num de VA", ylab = "Poisson(10000,0.85)")

Comparando plot de N = 15000

par(mfrow = c(3,2))
plot(mipoisson_l015_15000, col="blue", main = "15000 VA Pois(0.15)", xlab="Num de VA", ylab = "Poisson(15000,0.15)")
plot(mipoisson_l030_15000, col="blue", main = "15000 VA Pois(0.30)", xlab="Num de VA", ylab = "Poisson(15000,0.30)")
plot(mipoisson_l05_15000, col="blue", main = "15000 VA Pois(0.5)", xlab="Num de VA", ylab = "Poisson(15000,0.5)")
plot(mipoisson_l070_15000, col="blue", main = "15000 VA Pois(0.70)", xlab="Num de VA", ylab = "Poisson(15000,0.70)")
plot(mipoisson_l085_15000, col="blue", main = "15000 VA Pois(0.85)", xlab="Num de VA", ylab = "Poisson(15000,0.85)")

Comparación de gráficos Hist

Comparando hist de N = 100

par(mfrow = c(3,2))
hist(mipoisson_l015_100, col="lightgreen", main = "100 VA Pois(0.15)", xlab="VA generadas", ylab = "Poisson(100,0.15)")
hist(mipoisson_l030_100, col="lightgreen", main = "100 VA Pois(0.30)", xlab="VA generadas", ylab = "Poisson(100,0.30)")
hist(mipoisson_l05_100, col="lightgreen", main = "100 VA Pois(0.5)", xlab="VA generadas", ylab = "Poisson(100,0.5)")
hist(mipoisson_l070_100, col="lightgreen", main = "100 VA Pois(0.70)", xlab="VA generadas", ylab = "Poisson(100,0.70)")
hist(mipoisson_l085_100, col="lightgreen", main = "100 VA Pois(0.85)", xlab="VA generadas", ylab = "Poisson(100,0.85)")

Comparando hist de N = 500

par(mfrow = c(3,2))
hist(mipoisson_l015_500, col="lightgreen", main = "500 VA Pois(0.15)", xlab="VA generadas", ylab = "Poisson(500,0.15)")
hist(mipoisson_l030_500, col="lightgreen", main = "500 VA Pois(0.30)", xlab="VA generadas", ylab = "Poisson(500,0.30)")
hist(mipoisson_l05_500, col="lightgreen", main = "500 VA Pois(0.5)", xlab="VA generadas", ylab = "Poisson(500,0.5)")
hist(mipoisson_l070_500, col="lightgreen", main = "500 VA Pois(0.70)", xlab="VA generadas", ylab = "Poisson(500,0.70)")
hist(mipoisson_l085_500, col="lightgreen", main = "500 VA Pois(0.85)", xlab="VA generadas", ylab = "Poisson(500,0.85)")

Comparando hist de N = 1000

par(mfrow = c(3,2))
hist(mipoisson_l015_1000, col="lightgreen", main = "1000 VA Pois(0.15)", xlab="VA generadas", ylab = "Poisson(1000,0.15)")
hist(mipoisson_l030_1000, col="lightgreen", main = "1000 VA Pois(0.30)", xlab="VA generadas", ylab = "Poisson(1000,0.30)")
hist(mipoisson_l05_1000, col="lightgreen", main = "1000 VA Pois(0.5)", xlab="VA generadas", ylab = "Poisson(1000,0.5)")
hist(mipoisson_l070_1000, col="lightgreen", main = "1000 VA Pois(0.70)", xlab="VA generadas", ylab = "Poisson(1000,0.70)")
hist(mipoisson_l085_1000, col="lightgreen", main = "1000 VA Pois(0.85)", xlab="VA generadas", ylab = "Poisson(1000,0.85)")

Comparando hist de N = 5000

par(mfrow = c(3,2))
hist(mipoisson_l015_5000, col="lightgreen", main = "5000 VA Pois(0.15)", xlab="VA generadas", ylab = "Poisson(5000,0.15)")
hist(mipoisson_l030_5000, col="lightgreen", main = "5000 VA Pois(0.30)", xlab="VA generadas", ylab = "Poisson(5000,0.30)")
hist(mipoisson_l05_5000, col="lightgreen", main = "5000 VA Pois(0.5)", xlab="VA generadas", ylab = "Poisson(5000,0.5)")
hist(mipoisson_l070_5000, col="lightgreen", main = "5000 VA Pois(0.70)", xlab="VA generadas", ylab = "Poisson(5000,0.70)")
hist(mipoisson_l085_5000, col="lightgreen", main = "5000 VA Pois(0.85)", xlab="VA generadas", ylab = "Poisson(5000,0.85)")

Comparando hist de N = 10000

par(mfrow = c(3,2))
hist(mipoisson_l015_10000, col="lightgreen", main = "10000 VA Pois(0.15)", xlab="VA generadas", ylab = "Poisson(10000,0.15)")
hist(mipoisson_l030_10000, col="lightgreen", main = "10000 VA Pois(0.30)", xlab="VA generadas", ylab = "Poisson(10000,0.30)")
hist(mipoisson_l05_10000, col="lightgreen", main = "10000 VA Pois(0.5)", xlab="VA generadas", ylab = "Poisson(10000,0.5)")
hist(mipoisson_l070_10000, col="lightgreen", main = "10000 VA Pois(0.70)", xlab="VA generadas", ylab = "Poisson(10000,0.70)")
hist(mipoisson_l085_10000, col="lightgreen", main = "10000 VA Pois(0.85)", xlab="VA generadas", ylab = "Poisson(10000,0.85)")

Comparando hist de N = 15000

par(mfrow = c(3,2))
hist(mipoisson_l015_15000, col="lightgreen", main = "15000 VA Pois(0.15)", xlab="VA generadas", ylab = "Poisson(15000,0.15)")
hist(mipoisson_l030_15000, col="lightgreen", main = "15000 VA Pois(0.30)", xlab="VA generadas", ylab = "Poisson(15000,0.30)")
hist(mipoisson_l05_15000, col="lightgreen", main = "15000 VA Pois(0.5)", xlab="VA generadas", ylab = "Poisson(15000,0.5)")
hist(mipoisson_l070_15000, col="lightgreen", main = "15000 VA Pois(0.70)", xlab="VA generadas", ylab = "Poisson(15000,0.70)")
hist(mipoisson_l085_15000, col="lightgreen", main = "15000 VA Pois(0.85)", xlab="VA generadas", ylab = "Poisson(15000,0.85)")

En conclusión Poisson

Función rpois(n, lambda)

• n: Número de variables aleatorias a generar (tamaño de muestra)
• lambda (λ): Parámetro de la distribución de Poisson que representa la tasa promedio de ocurrencia de eventos en un intervalo determinado

Características principales: - La distribución de Poisson modela el número de eventos que ocurren en un intervalo fijo de tiempo o espacio - El parámetro λ es tanto la media como la varianza de la distribución - A medida que aumenta el número de muestras (N), la distribución se aproxima mejor a la forma teórica esperada - Con valores pequeños de λ (como 0.15 o 0.30), la distribución está más concentrada en valores bajos

• Con valores mayores de λ (como 0.70 o 0.85), la distribución se vuelve más simétrica y se dispersa más